U.S. Pat. Nos. 7,214,110 and 7,361,067, which are incorporated herein by reference, disclose acceleration control systems that allow the operator of a marine vessel to select an acceleration profile to control the engine speed of a marine vessel from an initial starting speed to a final desired speed. When used in conjunction with tow sports, such as wake boarding and water skiing, the use of acceleration profile provides consistent performance during the period of time when a water skier is accelerated from a stationary position to a full speed condition.